An athletic league does drug testing of its athletes, 10 percent of whom use drugs. This test, however, is only 95 percent reliable. That is, a drug user will test positive with probability 0.95 and negative with probability 0.05, and a nonuser will test negative with probability 0.95 and positive with probability 0.05.
Develop a probability tree diagram to determine the posterior probability of each of the following outcomes of testing an athlete.
(a) The athlete is a drug user, given that the test is positive.
(b) The athlete is not a drug user, given that the test is positive.
(c) The athlete is a drug user, given that the test is negative.
(d) The athlete is not a drug user, given that the test is negative.
(e) Use the Excel template for posterior probabilities to check your answers in the preceding parts.